Generator of numbers of oscillations

ABSTRACT

A circuit generates a number of oscillations. The circuit includes a first branch with at least one delay line introducing symmetrical delays on rising edges and on falling edges and at least one asymmetrical delay element introducing different delays on rising edges and on falling edges. The circuit further includes a second branch looped back on the first branch and including at least one delay line introducing symmetrical delays on rising edges and on falling edges.

PRIORITY CLAIM

This application claims the priority benefit of French Application forPatent No. 1654082, filed on May 4, 2016, the disclosure of which ishereby incorporated by reference in its entirety.

TECHNICAL FIELD

The present disclosure generally relates to electronic circuits and,more particularly, to circuits or electronic functions usable in acircuit or electronic device. An example of application of theelectronic circuits and functions of the present description is theforming of a random number generator. Another example of application isthe forming of a physical unclonable function (PUF), for example, togenerate unique identifiers or unique encryption keys. The presentdisclosure more particularly relates to random number generators insecurity applications such as ciphering, authentication, etc.

BACKGROUND

In many applications, processing units, for example, central processingunits (CPU) of microcontrollers, use randomly generated numbers.

Random number generation circuits use various circuits or subsets whichmay have other applications than random number generation. Inparticular, a random number generator uses circuits of oscillator,multiplexer, and the like type which, although they are particularlyadvantageous in random number generation, are not limited to suchapplications.

Number generators to which the present disclosure applies are based onthe use of delay lines looped back on each other.

There is a need to improve random number generators or circuitssupplying physical unclonable functions.

More generally, there is a need to improve logic electronic functions,usable not only in random or reproducible number generationapplications, but also in other applications where similar problems areposed.

SUMMARY

An embodiment overcomes all or part of the disadvantages of usualsolutions for generating random numbers or physical functions for uniqueidentifiers, encryption keys, etc.

An embodiment according to an aspect of the present disclosure providesa circuit having a behavior which can be modeled to form a generation ofnumbers of oscillations for random number or unclonable numbergeneration purposes.

An embodiment according to this aspect provides a generator having abehavior which can be verified.

An embodiment according to this aspect provides a solution compatiblewith the use of standard cells of a given electronic technology.

An embodiment according to another aspect of the present disclosureprovides a symmetrical multiplexer structure (that is a structure havinga similar behavior in time to conduct a rising edge and to conduct afalling edge).

An embodiment according to this other aspect provides a multiplexerstructure compatible with usual multiplexer structures.

An embodiment according to still another aspect of the presentdisclosure provides a counter of noisy signal state switching(oscillations).

An embodiment according to this still another aspect provides a solutionmore particularly adapted to the counting of an oscillation generator.

Thus, an embodiment of a first aspect provides a circuit for generatinga number of oscillations, comprising: a first branch comprising at leastone delay line introducing symmetrical delays on rising edges and onfalling edges and at least one asymmetrical delay element introducingdifferent delays on rising edges and on falling edges; a second branch,looped back on the first one and comprising at least one delay lineintroducing symmetrical delays on rising edges and on falling edges.

According to an embodiment of this first aspect, the second branchfurther comprises at least one asymmetrical delay element introducingdifferent delays on rising edges and on falling edges.

According to an embodiment of this first aspect, NAND-type gatescombining the respective outputs of the branches with a control signalare interposed between the respective outputs of each branch and theinput of the other branch.

According to an embodiment of this first aspect, the delay lines areformed of logic elements resulting in a single-input non-invertingfunction having identical rise and fall times.

According to an embodiment of this first aspect, the delay element(s)are formed of non-inverting logic circuits.

According to an embodiment of this first aspect, each delay element isformed of a logic function which can be reduced to a non-invertingfunction only depending on a single input and having different rise andfall times.

According to an embodiment of this first aspect, the one or morebranches further comprise a second delay line introducing symmetricaldelays on rising edges and on falling edges, connected in parallel onthe delay element of the concerned branch.

An embodiment also provides a number generator comprising: at least onecircuit for generating a number of oscillations; and at least onecounter of the number of oscillations generated by said circuit.

According to an embodiment, said circuit is configured to generate arandom number of oscillations.

An embodiment also provides an electronic device comprising at least onenumber generator configured to generate a reproducible number.

An embodiment of a second aspect provides a logic two-to-onemultiplexer, comprising: two input terminals; one output terminal; acontrol terminal; and a multiple of four series-connected two-to-onemultiplexers, a first multiplexer having its inputs connected to theinput terminals, a last unit multiplexer having its output connected tothe output terminal, and the other multiplexers having their respectiveinputs interconnected to the output of the previous multiplexer in theseries association, half of the multiplexers being controlled in reversewith respect to another half.

According to an embodiment of this second aspect, the multiplexers areinverting multiplexers.

According to an embodiment of this second aspect, all multiplexers areidentical.

According to an embodiment of this second aspect, half of themultiplexers have their control inputs connected to said controlterminal.

According to an embodiment of this second aspect, the other half of themultiplexers have their control inputs connected to the output of amultiplexer having an input connected to said control terminal.

An embodiment also provides a four-to-one multiplexer, comprising threetwo-to-one logic multiplexers.

An embodiment also provides a number generation circuit, comprising atleast one multiplexer such as hereinabove.

An embodiment of a third aspect provides a circuit for counting pulsessupplied by a circuit having at least two inverted pulse signal supplyterminals, comprising: a first counter of the pulses of a first pulsesignal supplying a first count; a second counter of the pulses of asecond pulse signal supplying a second count; and an element forselecting one of the counts.

According to an embodiment of this third aspect, the selection elementreceives, in addition to the counts supplied by the counters, said pulsesignals.

According to an embodiment of this third aspect, the selection elementtakes into account the disappearing of pulses of one of the pulsesignals.

According to an embodiment of this third aspect, the selected count isthat of the counter having the pulse signal which stops first.

According to an embodiment of this third aspect, the selected count isthat of the counter having the pulse signal which stops last.

According to an embodiment of this third aspect, the selected count isthat: of the counter having the highest count if the two counts have thesame parity; or of the counter having the highest count if this count iseven and the lowest one if the count is odd.

According to an embodiment of this third aspect, the selection circuitsupplies the least significant bit of the selected count.

According to an embodiment of this third aspect, the pulses are suppliedby two delay lines looped back on each other of an oscillationgenerator.

According to an embodiment of this third aspect, the pulse countingcircuit further comprises, upstream of each counter, a pulse shapingcircuit.

According to an embodiment of this third aspect, the shaping circuitcomprises a flip-flop having an output looped back on an initializationor reset (RN) input after crossing a delay element.

According to an embodiment of this third aspect, the delay introduced bythe delay element is greater than the minimum time for the flip-flop totake a pulse into account.

An embodiment also provides a number generation circuit, comprising atleast one pulse counting circuit.

The foregoing and other features and advantages will be discussed indetail in the following non-limiting description of specific embodimentsin connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the embodiments, reference will now bemade by way of example only to the accompanying figures in which:

FIG. 1 schematically shows in the form of blocks an embodiment ofelectronic circuit of the type to which the described embodiments apply;

FIG. 2 shows an example of a circuit for generating a number ofoscillations for a generator of random numbers or of an unclonablenumber;

FIGS. 3A, 3B, 3C, 3D, and 3E illustrate, in the form of timing diagram,a new interpretation of the operation of a generator of a number ofoscillations;

FIG. 4 shows an embodiment of an oscillation generator;

FIG. 5 schematically shows in the form of blocks an alternativeembodiment of a generator of a number of oscillations;

FIG. 6 schematically shows an embodiment of delay lines for a generatorof a number of oscillations;

FIG. 7 schematically shows an embodiment of two-to-one symmetricalmultiplexer circuit;

FIG. 8 shows an embodiment of a four-to-one symmetrical multiplexer;

FIG. 9 shows an embodiment of a random number generator based on agenerator of a number of oscillations;

FIG. 10 shows an embodiment of a pulse signal shaping circuit; and

FIGS. 11A, 11B, 11C, and 11D illustrate, in the form of timing diagrams,the operation of the shaping circuit of FIG. 10.

DETAILED DESCRIPTION

The same elements have been designated with the same reference numeralsin the different drawings. In particular, the structural and/orfunctional elements common to the different embodiments may bedesignated with the same reference numerals and may have identicalstructural, dimensional, and material properties. For clarity, onlythose steps and elements which are useful to the understanding of thedescribed embodiments have been shown and will be detailed. Inparticular, the uses of the generated numbers (random or unclonable) andthe applications of circuits integrating the described generator havenot been detailed, the described embodiments being compatible withcurrent uses and applications. Arbitrarily, the high state of a logicsignal is designated as 1 and its low state is designated as 0. Whenreference is made to terms “about”, “approximately”, or “in the orderof”, this means to within 10%, preferably to within 5%.

The number generator of the present disclosure is described hereafter inrelation with an example of a generator of random numbers ofoscillations. Unless otherwise specified, all that is describedhereafter however applies to a generator of a number of oscillations foran unclonable physical function.

FIG. 1 very schematically shows an electronic circuit 1 of the type towhich the embodiments which will be described apply.

Circuit 1 includes: a calculation or processing entity 12 (PU), forexample, a state machine, a microprocessor, a programmable logiccircuit, etc.; one or a plurality of volatile and/or non-volatilestorage areas 14 (MEM) for storing all or part of the data and keys; oneor a plurality of circuits 16 implementing various functions (FCT)related to the application for which circuit 1 is intended, for example,a cryptoprocessor, a biometric sensor control circuit, etc.; one or aplurality of data, address, and/or control buses 17 between thedifferent elements internal to circuit 1 and an input-output interface19 (I/O) for communicating with the outside of circuit 1; and one or aplurality of random number generation circuits 2 (RNG).

FIG. 2 shows an example of electric diagram of a usual generator 10 of anumber of oscillations for a random number generator.

Generator 10 is based on two delay lines, each formed ofseries-connected delay elements, looped back on each other, each delayelement returning the signal in the same state (1 or 0) as its input.The number of delay elements of each chain may be different oridentical. In the shown example, a first line 11 comprises fourseries-connected delay elements 111, 112, 113, and 114 between an outputterminal 131 of a first NAND-type logic gate 13 and a first inputterminal 153 of a second NAND-type logic gate 15. A second line 17comprises three series-connected delay elements 171, 172, and 173between an output terminal 151 of second gate 15 and a first input 133of first gate 13. The second respective inputs 135 and 155 of logicgates 13 and 15 form input terminals intended to receive a same controlsignal CTRL (for starting the generation of a number). The number ofoscillations, which conditions the random number, is sampled, forexample, on the output of the first line, that is, on first input 153 ofgate 15. As a variation, the number of oscillations is sampled on input133 of gate 13, at output 131 of gate 13, or at output 151 of gate 15.

The difference between the delays introduced by the two lines conditionsthe duty cycle of the signals present at terminals 133 and 153.

Theoretically, the generator of FIG. 2 oscillates indefinitely with aduty cycle as long as signal CTRL is at state 1. In practice, in theabsence of noise but with delay elements (logic gates) having differentdelays, which end up sufficiently deforming the duty cycle for theoscillator to stop, the generator ends up stopping after a fixed numberof oscillations. In the presence of noise (jitter), the generator endsup stopping, but after a number of oscillations having a variable value.Thus, the fact for the generator to stop is not a problem per se, on thecontrary, but the problem is not to be able to determine around whichvalue (what number of oscillations) it will stop. Indeed, in order forthe random number generator to operate properly, it must haveaccumulated enough noise, and thus a sufficient number of oscillationsso that the result of the counting of the number of oscillationsprovides, when the counter stops, enough randomness at the level of itsleast significant bit or of a few (less than ten) least significant bitsof the oscillation counter.

The above-described embodiments derive from a new analysis of thebehavior of a generator of numbers of oscillations.

In particular, the inventors have observed that it is possible to relatethe behavior of the generator of numbers of oscillations to theintrinsic quantifiable parameters of the elements forming it.

FIGS. 3A, 3B, 3C, 3D, and 3E illustrate in timing diagrams thetheoretical operation of the circuit of FIG. 2. FIG. 3A shows an exampleof shape of signal CTRL. FIG. 3B illustrates a corresponding example ofshape of the signal present on output 131 of gate 13. FIG. 3Cillustrates a corresponding example of shape of the signal present onthe output of the first line (input 133 of gate 13). FIG. 3D illustratesa corresponding example of shape of the signal present on output 151 ofgate 15. FIG. 3E illustrates a corresponding example of shape of thesignal present on the output of the first line (input 153 of gate 15).

The delay introduced by each gate and by each delay element is assumedto have a value tdu, identical for all elements and gates.

When signal CTRL is at state 0, outputs 131 and 151 are always atstate 1. Accordingly, outputs 133 and 153 of lines 17 and 11 are stableat state 1.

At a time t30, signal CTRL is switched to state 1 to activate thegeneration. After a delay tdu, outputs 131 and 151 switch to state 0 ata time t31. Lines 13 and 15 respectively introduce delays by 4*td_(u)and 3*td_(u) on the rising and falling edges of the signals present atterminals 131 and 151. Accordingly, signal 133 switches to state 1 at atime t32 subsequent by 3*td_(u) to time t31 and signal 153 switches tostate 1 at a time t33 subsequent by 4*td_(u) to time t31.

Signals 131 and 151 then switch to state 1 with a delay td_(u) withrespect to times t32 and t33 respectively, and so on.

The number of sampled oscillations, preferably at output 153 (or 133),when the oscillation stops, is random.

It should be noted that this number of oscillations may be counted atany point of the loop.

The inventors consider that, in addition to the phase noise, one of thefactors which results in stopping the generator particularly originatesfrom an imbalance between rise times and fall times of the signals, thatis, between the time taken by a delay element or a gate to switch fromstate 1 to state 0 and from state 0 to state 1. Indeed, the delaybetween the rise time and the fall time of a branch of the generator(delay line plus NAND gate) results in that there comes a time when theduration of a state becomes shorter than the delay introduced by anelement of the delay line.

A problem is that this “time” is a function of the number of delayelements in the line (accumulation of time shifts). It would however bedesirable for the duration at the end of which a generator stops to becontrollable, so as to, on design of a new circuit, be able to guaranteethat the number of oscillations before the stopping of the generator issufficient.

Taking the same notations as in the example of FIG. 2, the followingnotations will be used:

t1 _(n), the time of an edge (rising or falling) of rank n of the signalof output 131;

t2 _(n), the time of an edge (rising or falling) of rank n of the signalof output 151;

L1 _(n), the duration of the low level of rank n of the signal of output131 (this duration is linked to the delay introduced by second line 17plus first gate 13);

H2 _(n), the duration of the high level of rank n of the signal ofoutput 151 (this duration is linked to the delay introduced by firstline 11 plus second gate 15);

tr₁ and tf₁, the respective rise and fall times of the signal of output151 with respect to the switching time of terminal 131; and

tr₂ and tf₂, the respective rise and fall times of the signal of output131 with respect to the switching time of terminal 151.

The generator behavior may be written from arithmetic sequences.

In particular, the following can be written:L1_(n) =t1_(2n+1) −t1_(2n); andH2_(n) =t2_(2n+2) −t2_(2n+1).

Further:t1_(2n) =t2_(2n−1) +tf ₂;t1_(2n+1) =t2_(2n) +tr ₂;t2_(2n−1) =t1_(2n−2) +tr ₁; andt2_(2n) =t1_(2n−1) +tf ₁.

The following can be deduced:L1_(n) =H2_(n−1) −Δfr ₂, with Δfr ₂ =tf ₂ −tr ₂; andH2_(n−1) =L1_(n−1) +Δfr ₁, with Δfr ₁ =tf ₁ −tr ₁.

Based on these relations, the recurrences of the difference durationscan be simply expressed according to the differences between the riseand fall times.

For example, for duration, L1 _(n), one can write:L1_(n+1) =L1_(n) +Δfr ₁ −Δfr ₂.

Then, by expressing the sequence from the first term L1 ₀ (n=0):L1_(n) =L1₀ −n*r, with r=Δfr ₂ −Δfr ₁.

An arithmetic sequence having a common ratio r that can be determined,on design of the circuit, according to the number of selected basiccells (delay elements) and to their interval between rise time and falltime, is thus obtained.

A similar relation can be written for durations H2, with:H2_(n) =H2₀ −n*r.

Similarly, by noting:

H1 _(n), the duration of the high level of rank n of the signal ofoutput 131 (this duration is linked to the delay introduced by firstline 11 plus second gate 15);

L2 _(n), the duration of the low level of rank n of the signal of output151 (this duration is linked to the delay introduced by first line 11plus second gate 15);

the following relations can be obtained:H1_(n) =H1₀ +n*r; andL2_(n) =L2₀ +n*r.

If the difference between the rise times and the fall times (commonratio r) is negative, durations L1 and H2 increase while durations L2and H1 decrease. Conversely, if common ratio r is positive, durations L1and H2 decrease while durations L2 and H1 increase.

FIG. 4 shows an embodiment of a generator of numbers of oscillationstaking advantage of this analysis.

In practice, it is desired to be able to control (in order to respectthe characteristics desired for the random generator) the behavior alongtime of the oscillation generator, that is, the duration from which itstops. This duration is not only a function of the delay introduced bythe delay lines, but also of the rise and fall times of the lines.

Knowing the behaviors of the basic cells (delay elements) of thetechnology in which the random generator is desired to be formed, thenumber of oscillations after which the generator will stop can bededuced. With a positive common ratio r, a limit can be set whenduration L1 _(n) becomes zero, that is, for n=L1 ₀/r. In practice, theoscillations stop when the duration of the pulse becomes shorter thanthe delay of a delay element.

According to this embodiment, each branch is formed of a delay line 21,respectively 27, called symmetrical, that is, having identical or veryclose rise and fall times (interval between the rise and fall timeshorter than one tenth of common ratio r) in series with an element 22,respectively 28, called asymmetrical, having rise and fall timesdifferent from each other. An input terminal 231 of the first branch isconnected to the output of a first NAND-type logic gate 23 having afirst input 235 receiving a trigger signal CTRL and having a secondinput 233 receiving the output of the second branch. An output terminal253 of the first branch is connected to a first input of a secondNAND-type gate 25 having a first input 255 receiving signal CTRL andhaving its output 251 connected to the input of the second branch. Theoutput of the generator of a random number of oscillations is forexample terminal 253 or terminal 233. As previously, this output, andthus the oscillation counting, may correspond as a variation to output231 or 251 of gate 23, respectively 25, or more generally at any pointof the loop. In practice, the output is connected to the output of anasynchronous counter of the number of oscillations, which counts thenumber of oscillations between the activation of the generator by signalCTRL and the stopping of the oscillations. This counter (not shown inFIG. 4) is, for example, formed of a flip-flop or of a plurality offlip-flops in cascade, the clock input of the or of a first flip-flopreceiving the output signal of the generator. The flip-flop output(s)supply a number over one or a plurality of bits (according to the numberof flip-flops), where generally only the least significant bit(s) arekept to form the random number.

A plurality of generators may be used in parallel to increase the rateof generated random bits.

To form symmetrical delay lines 21 and 27, paired up inverters, that is,an even number of inverters in each line, are preferably used. Forexample, line 21 comprises p pairs of inverters 3 in series while line27 comprises q pairs of inverters 3 in series. Numbers p and q may beidentical or different from each other.

By using pairs of inverters, not only is there no inversion of thesignal at the output of each line, but above all, each line has anidentical or very close rise and fall time (interval smaller than onetenth of the common ratio divided by p or by q). Indeed, by usingidentical logic cells of the concerned technology, even if an inverter 3made in this technology has a rise time different from its fall time, apair of identical inverters 3 forms an element having identical rise andfall times. Noting tr and tf the rise and fall times of an inverter 3,the rise and fall times of a pair becomes tr+tf (tr+tf or tf+tr)according to the direction of the input edge). Thus, even if times tfand tr are different from each other, their sum remains constant for allthe inverter pairs. Lines 21 and 27 thus introduce a determinableconstant delay whatever the transition (rising or falling).

Any type of inverter may be used (for example, CMOS inverters formed oftwo series-connected transistors, NOR or NAND gates with interconnectedinputs, etc.), provided for these inverters to respect the condition ofassociating, when they are paired in series, successively the rise timeand the fall time, or conversely, so that these times are summed upwhatever the edge present at the input.

To form asymmetrical elements 22 and 24, a non-inverting element oflogic amplifier type (buffer) is used, excluding two identicalseries-connected inverters. For example, an OR-type, AND-type gatehaving its two inputs connected or also any logic function which may bereduced to an inverting function only depending on a single input andhaving different rise and fall times may be used. Each element 22 and 24is selected to have a rise time different from its fall time. Further,elements 22 and 24 are selected to have different intervals betweentheir rise time and fall time. Thus, the intervals which will conditionthe stopping of the generator are introduced. In practice, as appearsfrom the above-established formulas, gates 23 and 25 also introduce ashift between the rise and fall times of each branch. This shift shouldbe added to that introduced by element 24, respectively 22, to obtainintervals, respectively Δfr₁ and Δfr₂, and thus the common ratios of thearithmetic sequences.

An advantage of the provided embodiment is that numbers p and q of pairsof inverters of lines 21 and 27 have no influence on the common ratio ofthe arithmetic sequences defining the oscillations. Indeed, they onlycondition the first terms of each sequence, that is, the durations ofthe first pulses which follow the switching of signal CTRL to activatethe generation.

According to a simplified embodiment, a single element 22 or 24 isprovided, the other branch only having the symmetrical delay line.

Lines 21 and 27 may be indifferently placed upstream or downstream ofelements 22 and 24 with which they are respectively associated. As avariation, elements 22 and 24 are even interposed inside of lines 21 and27, between inverters or pairs of inverters forming them.

An advantage of the described embodiments is that it is now easy to sizean oscillation generator and to be able to characterize it. Thus, ondesign of an electronic circuit comprising a random number generator,knowing the intervals between the rise and fall times in the technology,it becomes easy to fulfill specifications.

The interpretation of the generated number is performed by counting thepulses on one of outputs 233 and 253 and by taking, as a random bit, forexample, the least significant bit at the end of the counting period.The counting period is set by a clock signal.

FIG. 5 schematically shows an alternative embodiment according to whichthe common ratio of the arithmetic sequence is desired to be minimized,while remaining easy to determine.

According to this variation, as compared with the embodiment of FIG. 4,one provides, in parallel with each element 22, 24 or asymmetrical delayline (ADL), a second symmetrical delay line (SDL) 26, respectively 28.The inputs of delay lines 22 and 26 are connected to the output of line21. The inputs of lines 24 and 28 are connected to the output of line27. The outputs of lines 22 and 26, respectively 24 and 28, areconnected to inputs of a two-to-one multiplexer 51, respectively 52,having its output connected to input 253, respectively 233, of logicgate 25, respectively 23. Multiplexer 51 is controlled by a signalresulting from a counting (counter 53, CNTH) of the pulses of its outputsignal. In other words, the counter determines the number of pulses fromwhich it is switched from asymmetrical line 22 to symmetrical line 26.On the side of multiplexer 52, a control by the same counter 53 or by adifferent counter which then counts the pulses of the output ofmultiplexer 52 may be provided. In practice, if a single counter isused, it is placed on the branch having the longest delay to avoidswitching the multiplexers before the end of the first pulses.

Such a variation enables to make the common ratio of the arithmeticsequences configurable and more particularly to decrease this commonratio to delay the stopping of the generator.

Indeed, executing an asymmetrical loop (a pulse on each branch) and therest of the loops only with the symmetrical elements (21, 26, 27 and 28)minimizes the common ratio of the sequence. Taking the above notations,common ratio r is divided by the number of loops. This enables, amongothers, to increase the number of pulses flowing through the delay linesof the generator while decreasing the size of the delay lines.

Counter 53 may be the counter counting the pulses having their leastsignificant bit(s) used, when the oscillations stop, to define thegenerated random number.

FIG. 6 shows an embodiment of a delay line 6, parameterizable both tohave a symmetrical delay and an asymmetrical delay.

The embodiment of FIG. 6 may form, as a specific example in the previousembodiments, an embodiment of the symmetrical delay line, for example,21, and of the asymmetrical delay element, for example, 22, of a branch.

According to this embodiment, one or a plurality (in the example, three)symmetrical delay lines 212, 214, and 216, that is, each havingidentical rise and fall times, are associated with one or a plurality(in the example, three) delay elements or asymmetrical delay lines 221,223, 225, that is, each having different rise and fall times, eachasymmetrical or symmetrical line being bypassable by means of amultiplexer 61, 62, 63, 64, 65, 66, respectively. In other words, theinputs of lines 212, 214, 216, 221, 223, and 225 are respectivelyconnected to a first input of multiplexers 61, 62, 63, 64, 65, 66 havingits other input connected to the output of the corresponding delay line.The outputs of multiplexers 61, 62, 63, 64 and 65 are respectivelyconnected to the inputs of lines 214, 216, 221, 223, 225 and the outputof multiplexer 66 defines output OUT of the parameterizable delay line.

Each multiplexer 61 to 66 is individually controllable, for example, bya different bit, respectively bit 5, bit 4, bit 3, bit 2, bit 1, and bit0, of a word SEL_DLY.

In an application to the forming of a generator of numbers ofoscillations of the type illustrated in FIG. 4, input terminal IN ofline 6 is connected to the output (231 or 251, FIGS. 4 and 5) of theconcerned branch.

Each line 212, 214, 216 is preferably formed of one or a plurality ofinverter pairs, that is, of delay elements, each having identical riseand fall times as described hereabove. In the shown example, lines 212,214 and 216 respectively comprise 32, 16 and 8 pairs of inverters, thatis, 32, 16 and 8 unit symmetrical delay elements (sdelt).

Asymmetrical lines 221, 223, 225 introduce identical or differentdelays. Preferably, lines 221, 223, and 225 are formed of identical unitelements, that is, introducing the same shift between rise time and falltime. Different numbers of the unit elements are then provided in eachof the lines, which makes the system easily parameterizable with anoptimal granularity. In the shown example, lines 221, 223, and 225respectively comprise 4, 2, and 1 asymmetrical unit delay elements(adelt).

Thus, the delay and the difference between rise time and fall time ofdelay line 6 can both be parameterized. Taking the example of identicalunit elements in lines 212, 214, and 216 and of identical unit elementsin lines 221, 223, and 225, a symmetrical delay in the range from 8 to56 times the delay of the symmetrical unit element and a time intervalbetween the rising edge and the falling edge in the range from 1 to 7times the interval introduced by the symmetrical unit element may beselected.

The unit elements are for example formed as described hereinabove inrelation with FIG. 4.

The number of symmetrical and asymmetrical delay lines depends on thedesired adjustment capacity. The asymmetrical elements have not onlydifferent rise and fall times, but also an intrinsic delay whichcontributes to the total delay of the delay line.

The embodiment of FIG. 6 may for example be used to integrate a samegenerator architecture and to make this structure parameterizable, be iton design or in the application.

The embodiment of FIG. 6 may be combined with that of FIG. 5 by placing,in parallel with each asymmetrical line 221, 223, 225, a symmetricalline of same delay, thus suppressing the bypass of the line driving theupper inputs (in the orientation of FIG. 6) of multiplexers 64 to 66. Asa variation, 3-to-1 multiplexers having two inputs receiving therespective outputs of two lines in parallel of same delay, respectivelysymmetrical and asymmetrical, and having the third input directlyreceiving the output of the multiplexer of previous rank, are used.

In the embodiment of FIG. 6 or of its variations, to make theparameterizing easier, it would be desirable for multiplexers 61 to 66to introduce symmetrical delays. Now, a usual multiplexer has anasymmetrical operation in terms of rise time and of fall time.

FIG. 7 shows an embodiment of a multiplexer 7 having a symmetricaloperation, that is, identical rise and fall times.

Multiplexer 7 or FIG. 7 is a two-to-one multiplexer, that is, it selectsone of its two inputs A or B and supplies the corresponding signal atoutput Z. The selection between A or B is performed by a control signalS.

Multiplexer 7 comprises four two-to-one multiplexing or selectionelements. Multiplexer 7 can be considered as being formed of 4 unitmultiplexers 72, 74, 76, and 78 associated in a chain. The multiplexersare inverting multiplexers. A first multiplexer 72 has its inputterminals respectively connected to inputs A and B. A second multiplexer74 has its two inputs connected together to the output of firstmultiplexer 72. A third multiplexer 76 has its two inputs connectedtogether to the output of second multiplexer 74. A fourth multiplexer 78has its two inputs connected together to the output of third multiplexer76 and its output delivers output Z. Signal S directly controlsmultiplexers 72 and 74 and, after having crossed an inverter 75,multiplexers 76 and 78.

The fact for multiplexers 74, 76, and 78 to have their inputsinterconnected results in that they actually perform no selection.However, assuming that all multiplexers 72, 74, 76, and 78 areidentical, they all have identical rise and fall times. Further, theyall have a similar behavior in the presence of an edge on their firstinput and all have a similar behavior in the presence of an edge ontheir second input.

Noting tr the rise times, tf the fall times, and by adding to thesenotations a first index A, respectively B, according to whether the edgeis on input A (the first input of the concerned multiplexer) or B (thesecond input of the concerned multiplexer) and a second index 72, 74,76, or 78 according to the concerned multiplexer, one may write:tr _(A72) =tr _(A74) =tr _(A76) =tr _(A78) =tr _(A);tf _(A72) =tf _(A74) =tf _(A76) =tf _(A78) =tf _(A);tr _(B72) =tr _(B74) =tr _(B76) =tr _(B78) =tr _(B); andtf _(B72) =tf _(B74) =tf _(B76) =tf _(B78) =tf _(B).

Due to the inversion of the control of the two multiplexers 76 and 78with respect to that of multiplexers 72 and 74, the rise and fall timesof multiplexer 7, from input A or B to output Z, may be writtenaccording to whether a rising edge r or falling edge f is present oninput A or on input B:tr _(AZ) =tf _(A72) +tr _(A74) +tf _(B76) +tr _(B78);tf _(AZ) =tf _(A72) +tf _(A74) +tr _(B76) +tf _(B78);tr _(BZ) =tf _(B72) +tr _(B74) +tf _(A76) +tr _(A78); andtf _(BZ) =tf _(B72) +tf _(B74) +tr _(A76) +tf _(A78).

Since the unit rise and fall times are identical for a given input, onecan deduce:tr _(AZ) =tf _(AZ) =tr _(BZ) =tf _(BZ) =tr _(A) +tf _(A) +tr _(B) +tf_(B).

Accordingly, the rise and fall times of multiplexer 7 are identicalwhatever the considered input. The multiplexer is thus symmetrical withthe above given definition.

As a variation, it may be provided to invert the control in otherlocations, provided for the two multiplexers to select their firstrespective inputs when the two others select their second respectiveinputs. In this case, it will however be ascertained that thepropagation delay introduced by the inverters is not greater than theminimum propagation time of a unit multiplexer, short of which theoutput is altered. An advantage of the embodiment of FIG. 7 is that itguarantees that the selection of multiplexers 76 and 78 is active beforethe signal (the edge) has ended crossing multiplexers 72 and 74.

Although this provides no advantage in terms of symmetry, it may beprovided to use 8, 12, 16, and more generally any multiple of four unitmultiplexers, provided for half of them to be controlled in reverse withrespect to the other half. This, for example, enables to increase thepropagation time without altering the symmetry of the operation.

An advantage of the embodiment of FIG. 7 is that it is independent fromthe internal structure of the unit multiplexers. Indeed, provided to useidentical unit multiplexers, the described operation is respected.

A multiplexer such as shown in FIG. 7 has multiple applications. Inparticular, it is frequently advantageous to have a symmetricaloperation.

As a specific example of application, the multiplexer of FIG. 7 may beused to form each of multiplexers 61, 62, 63, 64, 65 and 66 of theembodiment of FIG. 6. An advantage then is that the common ratio of thepulse sequences of the number generator remains only linked toasymmetrical elements 221, 223 and 225, which eases the sizing.

The structure of multiplexer 7 of FIG. 7 may be adapted to formmultiplexers with more than two inputs.

FIG. 8 shows an embodiment of a symmetrical four-to-one multiplexer 8.

According to this embodiment, three two-to-one multiplexers of the typeof that in FIG. 7 are used. A first multiplexer 7 a defines two inputs Aand B. A second multiplexer 7 b defines inputs C and D. The respectiveoutputs of multiplexers 7 a and 7 b are connected to the two inputs of athird multiplexer 7 c having its output defining output Z′ of thefour-to-one multiplexer. Multiplexers 7 a and 7 b are respectivelycontrolled by a signal S1 and by its inverse. Multiplexer 7 c iscontrolled by a signal S2. For example, assuming a selection word overtwo bits, signal S2 is formed by the most significant bit and signal S1is formed by the least significant bit.

In a random number generator of the above-described type, theinterpretation of the generator output requires counting the pulsespresent at the output. This counting determines the drawn number. Forexample, the least significant bit of the count of the pulses present atthe generator output between the starting thereof and a read signal ofthe counter, subsequent to the stopping of the oscillations, is taken asthe random bit generated by generator 20. The time interval between thestarting of the generator and the read signal is selected according tothe range of possible time intervals conditioned by the sizing of thedelay lines of the generator.

However, in a counter, there may be an imbalance between the counts ofstate 1 and of states 0, in particular if one of the states of thesignal to be counted becomes too short with respect to the other. Thisphenomenon is due to the fact that from a given pulse duration (in thedirection of decreasing durations), the counter is only capable oftaking into account the pulse in one direction according to the parityof the current count that it contains. There then is an imbalancebetween the probability of drawing a 1 and of drawing a 0. In otherwords, with a generator of the type in FIG. 4 (but also with that inFIG. 2), when the duty cycle becomes too deformed, the use of thegenerator output as a counting clock results in that the duration of thepulse (low or high according to the concerned output) is shorter thanthe minimum time required the flip-flop to take it into account. Now,this time differs for a high state and for a low state. Accordingly,whatever the output used, the flip-flop will leave its normal operationand one cannot determine in advance, on design, which output will beconcerned.

This problem may be encountered not only to count the number ofoscillations in a generator such as described in the present disclosure,but more generally to count events of short duration in a signal, forexample, a glitch detector.

Indeed, a counter, be it asynchronous or not, operates normally with aclock, called square, that is, having a duty cycle close to 50%. Now, inthe case of the above-described generator, the duty cycle of the clockof the asynchronous counter, which corresponds to output 231 or 251 (or233, 253), decreases at each period until the end of the oscillation, oron the contrary increases at each period until the end of theoscillation. Accordingly, one of the outputs stops at step 0 and theother stops at state 1. However, one can generally not know withcertainty which of the outputs will stop at state 1 and which one willstop at state 0.

On the counter side, flip-flops which require in their specifications aminimum duration of the clock in the high state (1) and a minimumduration of the clock signal in the low state (0), for example,arbitrarily 110 ps for the minimum duration in the high state and 87 psfor the minimum duration in the low state, are used. Accordingly, whenthe input flip-flop of the counter receives a clock having a very low orvery high duty cycle, it may end up operating outside of thespecifications and the pulse of the clock signal is then not taken intoaccount.

FIG. 9 shows an embodiment of a random number generator of theabove-described type with its pulse counting elements enabling to shapethe generated number.

FIG. 9 illustrates a variation where the numbers of generated pulses aresampled from the output of gates 231 and 251.

According to this embodiment, each output 251, 231 of the randomoscillation number generator 20 (RONG), for example, such as describedin FIG. 4, is connected to the input of a counter, respectively 91(CNTR), 93 (CNTL). Each counter 91, 93 counts the pulses of thecorresponding generator output signal. Each counter is an asynchronouscounter, for example, of D flip-flop type.

The reading of counters 91 and 93 is triggered by a signal READ whichtransfers the counts to a decision (DECIS) or combination circuit 95.Circuit 95 also receives output signals 231 and 251 to know, at the timeof the decision, the states of these signals when the oscillations stop.

Functionally, counters of the number of oscillations are used, one withan output of generator 20, the other with the other output of generator20. As indicated hereinabove, one of the counters will stop operatingbefore the other, that is, its input flip-flop will stop operatingbefore the input flip-flop of the other one, due to the fact that theminimum operating durations of the flip-flops are different for the lowstate and for the high state. In fact, one of the counters will stopunder the effect of an oscillation which does not respect its minimumtime in the low state while the other counter will stop under the effectof an oscillation which does not respect its minimum time in the highstate.

According to applications, the criterion of selection by circuit 95between the outputs of counters 91 and 93 according to the statessupplied by outputs 231 and 251, differs. Such a selection criterion maybe conditioned by a simulation of the generator operation to determinewhether the flip-flops stop because of the minimum time in the highstate or because of the minimum time in the low state.

For example, if importance is given to the parity of the counting resultand assuming that the flip-flop of the counter which stops first stopsunder the effect of too short a duration in the low state (state 0), thevalue of the corresponding counter will be lower than the value of theother counter. If this effect is cumulated with an asymmetricaloperation of the flip-flop, that is, an easier switching from 0 to 1than from 1 to 0 (or conversely), this introduces a bias in the randomnumber generation, which is not desirable. That of the counters whichhas stopped on a switching from 1 to 0 is then selected.

According to still another example where the parity has less importancethan a high number of oscillations, the counter which stops last isselected.

According to still another example, the decision depends on the relationbetween counters. Thus, one keeps the value: of the counter having thehighest count if the two counts have the same parity; or of the counterhaving the highest count if this count is even and the lowest one if thecount is odd.

According to still another example, it is considered that that of thecounters which keeps on operating has a high risk of operatingasymmetrically since the other counter has already stopped. In thiscase, block 95 selects the result of the counter which stops first, thatis, the first one which, on state switching of output 231 or 251, doesnot change its least significant bit. This embodiment is preferred inthe case where the cause of the stopping of the flip-flops (minimum timein the low state or minimum time in the high state) has not beendetermined by simulation.

The fact of counting the two outputs and of taking one or the otheraccording to cases enables to miss no pulse.

It should be noted that the counting circuit described in relation withFIG. 9 more generally applies to any random number generator and notnecessarily to that of FIG. 4. In particular, it may be implemented forany random number generator having delay lines looped back on each other(for example, FIG. 2).

According to another embodiment of this counting aspect, the signalssupplied by outputs 253 and 233 are shaped before being counted toeliminate possible miscounts. To achieve this, optional shaping circuits(SHAPER) 97 are interposed between respective outputs 251 and 231 andcounters 91 and 93.

FIG. 10 shows an embodiment of a pulse signal shaping circuit 97.

Circuit 97 comprises a D-type flip-flop 972 having its D input forced tothe high state (1) and having its Q non-inverted output defining outputS97 supplying the shaped signal. The CK clock input of flip-flop 972defines the input of the circuit receiving the pulse signal to beshaped. The NQ inverted output of flip-flop 972 is connected, via anon-inverting delay element 974 (DELAY), to a first input of an AND-typelogic gate 976 having an output connected to the RN reset input (activeon the rising edge) of flip-flop 972. A second input of gate 976 isintended to receive a signal RSTN for activating circuit 97. When signalRSTN is at state 0, circuit 97 is not active and output S97 ispermanently at state 0. Gate 976 is thus optional if circuit 97 does notneed to be deactivated.

The value of the delay introduced by element 974 is selected to begreater than the minimum pulse width that can be captured by the Dflip-flop.

FIGS. 11A, 11B, 11C and 11D illustrate, in the form of timing diagrams,the operation of the shaping circuit of FIG. 10. FIG. 11A shows anexample of shape of input signal CK to be shaped. FIG. 11B shows anexample of corresponding shape of the signal of the Q output (S97). FIG.11C shows an example of corresponding shape of the NQ output. FIG. 11Dshows an example of corresponding shape of the signal of the RN input.

A pulse signal CK of positive pulses is assumed.

Initially, the Q output (and thus output S97) is at state 0, the NQoutput is at state 1. The RN input is at state 1. Signal RSTN is assumedto be active (state 1).

On occurrence (time t90) of a rising edge on clock signal CK, since theD input is at state 1 and the RN input is at state 1, this pulse istransmitted onto the Q output which switches to state 1. However, the NQoutput (inverse of the Q output) switches to state 0. This state istransmitted, with a delay DELAY on the RN input (considering the delayintroduced by gate 976 included in value DELAY). The switching of the RNinput at the end of delay DELAY causes the forcing of the Q output tostate 0 and, accordingly, of the NQ output to state 1, which causes, inturn, always at the end of delay DELAY, a switching of the RN input tostate 0. The flip-flop is then ready to take a new state into account.The right-hand portion of the timing diagrams illustrates the operationwith a pulse CK having a duration shorter than delay DELAY. Delay DELAYsets the duration of the pulses of the output signal independently fromthe duration of the pulse of signal CK. Accordingly, even if the pulseof signal CK is theoretically too short for its fall to be taken intoaccount, it is still present on the Q output.

Duration DELAY sets the duration of the pulses of signal S97, and thusof input of the counters in the embodiment of FIG. 10.

To form a shaping circuit operating with a pulse signal of negativepulses, the output of gate 976 is connected to the set input of theflip-flop, the input is forced to state 0, and the delay elementreceives the Q non-inverted output while the output of the shapingcircuit is defined by the NQ inverted output. The operation can beeasily transposed from the above explanations.

An advantage of the embodiments which have been described is that theyenable to reliably design or to configure a random number generator indeterminable fashion. Thus, the criteria set by specifications can befulfilled and the fact for the generator to fulfill these specificationscan be validated.

Another advantage is that the described solution is compatible with theuse of standard cells of a given technology.

Another advantage is that the generator assembly can be formed withlogic elements.

For a random number generator, the number is sampled either after afixed time interval, started by the activation of the generator (signalCTRL) and selected to be greater than the maximum stop time of thegenerator, or by detecting the stopping of the counter(s).

To form a generator of unclonable numbers of integrated circuitidentifier type, the delay lines and the common ratio of the arithmeticsequences are sized to set the number of oscillations. The number issampled after the stopping of the generator in the same way as for arandom number generator and only part of the bits are preferably kept(the most significant).

Various embodiments have been described. Various alterations,modifications, and improvements will occur to those skilled in the art.In particular, the selection of the delays introduced by the symmetricaldelay lines and of the shifts introduced by the asymmetrical delayelements depends on the application and on the specifications of thegenerator. Finally, the practical implementation of the embodimentswhich have been described is within the abilities of those skilled inthe art based on the functional indications given hereabove.

Such alterations, modifications, and improvements are intended to bepart of this disclosure, and are intended to be within the spirit andthe scope of the present invention. Accordingly, the foregoingdescription is by way of example only and is not intended to belimiting. The present invention is limited only as defined in thefollowing claims and the equivalents thereto.

What is claimed is:
 1. A circuit for generating a number ofoscillations, comprising: a first circuit branch comprising at least onedelay line configured to introduce symmetrical delays on rising edgesand on falling edges and at least one asymmetrical delay elementconfigured to introduce different delays on rising edges and on fallingedges; a second circuit branch that is looped back on the first circuitbranch and comprising at least one delay line introducing symmetricaldelays on rising edges and on falling edges; and NAND-type gatesconfigured to combine respective outputs of the first and secondbranches with a control signal, said NAND-type gates being interposedbetween the respective outputs of one of the first and second branchesand respective inputs of another one of the first and second branches.2. The circuit of claim 1, wherein the second circuit branch furthercomprises at least one asymmetrical delay element introducing differentdelays on rising edges and on falling edges.
 3. The circuit of claim 1,wherein each delay line is formed of logic elements equivalent to asingle-input non-inverting function having identical rise and falltimes.
 4. The circuit of claim 1, wherein each delay line is formed ofone or more non-inverting logic circuits.
 5. The circuit of claim 4,wherein each delay line is formed of a logic function which can bereduced to a non-inverting function only depending on a single input andhaving different rise and fall times.
 6. The circuit of claim 2, whereinthe first and second circuit branches each further comprise a seconddelay line introducing symmetrical delays on rising edges and on fallingedges, said second delay line being connected in parallel with the atleast one asymmetrical delay element of the first circuit branch andconnected in parallel with the at least one asymmetrical delay elementof the second circuit branch.
 7. A number generator, comprising: atleast one circuit for generating a number of oscillations, comprising: afirst circuit branch comprising at least one delay line configured tointroduce symmetrical delays on rising edges and on falling edges and atleast one asymmetrical delay element configured to introduce differentdelays on rising edges and on falling edges; and a second circuit branchthat is looped back on the first circuit branch and comprising at leastone delay line introducing symmetrical delays on rising edges and onfalling edges; and at least one counter configured to count a number ofoscillations generated by said at least one circuit.
 8. The generator ofclaim 7, wherein the second circuit branch further comprises at leastone asymmetrical delay element introducing different delays on risingedges and on falling edges.
 9. The generator of claim 7, furthercomprising NAND-type gates configured to combine respective outputs ofthe first and second branches with a control signal, said NAND-typegates being interposed between the respective outputs of one of thefirst and second branches and respective inputs of another one of thefirst and second branches.
 10. The generator of claim 7, wherein eachdelay line is formed of logic elements equivalent to a single-inputnon-inverting function having identical rise and fall times.
 11. Thegenerator of claim 7, wherein each delay line is formed of one or morenon-inverting logic circuits.
 12. The generator of claim 11, whereineach delay line is formed of a logic function which can be reduced to anon-inverting function only depending on a single input and havingdifferent rise and fall times.
 13. The generator of claim 8, wherein thefirst and second circuit branches each further comprise a second delayline introducing symmetrical delays on rising edges and on fallingedges, said second delay line being connected in parallel with the atleast one asymmetrical delay element of the first circuit branch andconnected in parallel with the at least one asymmetrical delay elementof the second circuit branch.
 14. The generator of claim 7, wherein thenumber of oscillations is a random number of oscillations.
 15. Thegenerator of claim 7, wherein the count is a reproducible number. 16.The generator of claim 13, further comprising: a multiplexer having afirst input coupled to an output of the second delay line and a secondinput coupled to an output of the at least one asymmetrical delayelement of the first circuit branch, wherein an output of themultiplexer is coupled to an input of the second circuit branch; andwherein the multiplexer is controlled by an output of the at least onecounter.
 17. A circuit for generating a number of oscillations,comprising: a first circuit branch comprising: at least one firstsymmetrical delay line configured to introduce symmetrical delays onrising edges and on falling edges; at least one first asymmetrical delayline, connected in series with the at least one first symmetrical delayline, configured to introduce different delays on rising edges and onfalling edges; and at least one second symmetrical delay line, connectedin parallel with the at least one first asymmetrical delay line,configured to introduce symmetrical delays on rising edges and onfalling edges; a second circuit branch that is looped back on the firstcircuit branch and comprising at least one third symmetrical delay lineconfigured to introduce symmetrical delays on rising edges and onfalling edges.
 18. The generator of claim 17, further comprising a firstmultiplexer having a first input coupled to an output of the at leastone first asymmetrical delay line, a second input coupled to an outputof the at least one second symmetrical delay line; and an output coupledto an input of the second circuit branch.
 19. The generator of claim 18,wherein the first multiplexer further has a control input configured toreceive a selection signal, the first multiplexer operating in responseto the selection signal to selectively connect one of the first andsecond inputs of the first multiplexer to the output of the firstmultiplexer.
 20. The generator of claim 19, further comprising a firstNAND gate having a first input coupled to the output of the firstmultiplexer, and second input configured to receive a control signal andan output coupled the input of the second circuit branch.
 21. Thegenerator of claim 19, further comprising a counter circuit configuredto count oscillations at the output of the first multiplexer and havingan output generating the selection signal.
 22. The generator of claim17, further comprising at least one second asymmetrical delay line,connected in parallel with the at least one second symmetrical delayline, introducing different delays on rising edges and on falling edges.23. The generator of claim 22, further comprising a second multiplexerhaving a first input coupled to an output of the at least one secondasymmetrical delay line, a second input coupled to an output of the atleast one third symmetrical delay line; and an output coupled to aninput of the first circuit branch.
 24. The generator of claim 23,wherein the second multiplexer further has a control input configured toreceive a selection signal, the second multiplexer operating in responseto the selection signal to selectively connect one of the first andsecond inputs of the second multiplexer to the output of the secondmultiplexer.
 25. The generator of claim 24, further comprising a secondNAND gate having a first input coupled to the output of the secondmultiplexer, and second input configured to receive a control signal andan output coupled to the input of the first circuit branch.
 26. Thegenerator of claim 24, further comprising a counter circuit configuredto count oscillations at the first circuit branch and having an outputgenerating the selection signal.
 27. A circuit for generating a numberof oscillations, comprising: a first circuit branch comprising at leastone delay line configured to introduce symmetrical delays on risingedges and on falling edges and at least one asymmetrical delay elementconfigured to introduce different delays on rising edges and on fallingedges; and a second circuit branch that is looped back on the firstcircuit branch and comprising at least one delay line introducingsymmetrical delays on rising edges and on falling edges and at least oneasymmetrical delay element introducing different delays on rising edgesand on falling edges; and wherein the first and second circuit brancheseach further comprise a second delay line introducing symmetrical delayson rising edges and on falling edges, said second delay line beingconnected in parallel with the at least one asymmetrical delay elementof the first circuit branch and connected in parallel with the at leastone asymmetrical delay element of the second circuit branch.
 28. Thecircuit of claim 27, wherein the at least one delay line configured tointroduce symmetrical delays on rising edges and on falling edges and atleast one asymmetrical delay element configured to introduce differentdelays on rising edges and on falling edges of the first circuit branchare coupled in series; and wherein the at least one delay lineintroducing symmetrical delays on rising edges and on falling edges andat least one asymmetrical delay element introducing different delays onrising edges and on falling edges of the second circuit branch arecoupled in series.
 29. The circuit of claim 27, further comprisingNAND-type gates configured to combine respective outputs of the firstand second branches with a control signal, said NAND-type gates beinginterposed between the respective outputs of one of the first and secondbranches and respective inputs of another one of the first and secondbranches.
 30. The circuit of claim 27, wherein each delay line is formedof logic elements equivalent to a single-input non-inverting functionhaving identical rise and fall times.
 31. The circuit of claim 27,wherein each delay line is formed of one or more non-inverting logiccircuits.
 32. The circuit of claim 31, wherein each delay line is formedof a logic function which can be reduced to a non-inverting functiononly depending on a single input and having different rise and falltimes.